For each n≥1, we introduce two new Segal-type models of n–types of topological spaces: weakly globular n–fold groupoids and their lax version. We show that any n–type can be represented up to homotopy by such models via an explicit algebraic fundamental n–fold groupoid functor. We compare these models to Tamsamani’s weak n–groupoids, and extract from them a model for (k−1)–connected n–types.
|Number of pages||73|
|Journal||Algebraic and Geometric Topology|
|State||Published - 15 Jan 2015|
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- Algebraic model
- N–fold groupoid
- Weakly globular
ASJC Scopus subject areas
- Geometry and Topology